A method and system for predicting adverse drug reactions with delayed feedback

Abstract

The present invention relates to a method and system for predicting adverse drug reactions with delayed feedback, belonging to the technical field of adverse drug reaction prediction, and solves the problem of inaccurate prediction in the prior art. The method includes the following steps: obtaining characteristic data and observation data of drugs and adverse reactions, and constructing a training sample set; constructing a joint learning model, the joint training model includes: a propensity score model for predicting the probability that a drug-adverse reaction is observed; an adverse reaction prediction model for predicting the probability that a drug produces an adverse reaction; a delayed feedback prediction model for predicting the delayed feedback time of an adverse reaction; training the joint learning model based on the constructed training sample set to obtain a trained joint learning model; inputting the characteristic data of the drug and adverse reaction to be predicted into the trained joint learning network to predict whether the drug will cause the adverse reaction. Accurate and unbiased prediction of adverse drug reactions is achieved.

Description

Technical Field

[0001] The present invention relates to the technical field of adverse drug reaction prediction, and particularly to a method and system for predicting adverse drug reactions with delayed feedback. Background Art

[0002] Adverse drug reactions (ADRs, also known as side effects) refer to harmful effects on patients' treatment during conventional drug treatment. To date, thousands of types of adverse reactions have been reported, many of which have led to serious unexpected and harmful consequences. Timely and effective ADR warnings help standardize and guide the production of drugs with limited side effects. In the problem of predicting adverse drug reactions, the same drug may cause multiple adverse reactions, but the number of types of adverse reactions is much larger than the possible adverse drug reactions caused by a single drug, resulting in a sparsity problem in the data of adverse drug reactions. Many previous methods have been based on association rule mining and statistical significance testing to identify significant associations between drugs and ADRs, but their performance in prediction tasks is limited. Another class of deep learning-based methods uses pharmacovigilance networks, ensemble methods, and deep neural network models, achieving good prediction performance in specific adverse reaction predictions. However, since a drug may cause multiple ADRs simultaneously, directly reusing single-label prediction methods without considering the deep connections between drug-drug, ADR-ADR, and drug-ADR may result in time-consuming and poor prediction performance.

[0003] Accurately predicting the probability of a specific drug producing a specific adverse reaction can guide the production of new drugs, minimizing the probability of (severe) adverse reactions in new drugs.

[0004] In practical applications, high-quality explicit feedback may be lacking. Instead, there is a large amount of implicit feedback in the data. For example, in an adverse drug reaction system, the way to collect adverse reactions caused by drugs is usually through user reports, and not all adverse reactions of each drug can be captured. One of the most serious problems of implicit feedback is the existence of selection bias. In other words, the collected drug-adverse reaction pairs are usually a set of "non-randomly missing" samples of the overall sample: in an adverse reaction reporting system, more severe adverse reactions have a greater probability of being reported, while milder adverse reactions are easily overlooked. Therefore, directly exploring the relationship between drugs and adverse reactions from the observed drug-adverse reaction pairs may lead to a decline in the performance of the drug-adverse reaction prediction model. For example, for drugs used to treat cancer or leukemia, some severe adverse reactions will be reported (such as shock or massive bleeding), while some milder adverse reactions (such as stomachache, dizziness) will not be reported even if they occur, resulting in negative samples for both the unreported but occurred adverse reactions and the unoccurred adverse reactions in the observed data, thus leading to the selection bias problem.

[0005] To address the selection bias of implicit feedback, traditional feature engineering-based methods collect the feature information of drugs and adverse reactions and use the combination of these features to predict drug adverse reactions. In addition, some collaborative filtering methods such as matrix factorization (MF) and neural matrix factorization (NMF) can capture the potential connections between drugs and adverse reactions. These methods have been widely used to handle implicit feedback. However, previous methods have ignored the problem of delayed feedback, which often occurs in real-world scenarios. In the prediction of drug adverse reactions, since it takes a certain amount of time for an individual to develop an adverse reaction after taking a certain drug, and the conversion time of this part may be too long to exceed the observation time of the adverse reaction reporting system, resulting in these drug adverse reaction pairs that should be positive samples being marked as negative samples in the system, leading to the generation of false negative samples and further causing sample bias. Ignoring delayed feedback in predicting drug adverse reactions will lead to inaccurate predictions. Summary of the Invention

[0006] In view of the above analysis, embodiments of the present invention aim to provide a method and system for predicting drug adverse reactions with delayed feedback to solve the problem of inaccurate prediction of drug adverse reactions when there are both selection bias and delayed feedback.

[0007] On the one hand, embodiments of the present invention provide a method for predicting drug adverse reactions with delayed feedback, including the following steps:

[0008] Obtain the feature data and observation data of drugs and adverse reactions, and construct a training sample set;

[0009] Construct a joint learning model, where the joint training model includes: a propensity score model for predicting the probability that a drug-adverse reaction is observed; an adverse reaction prediction model for predicting the probability that a drug produces an adverse reaction; a delayed feedback prediction model for predicting the delayed feedback time of the adverse reaction;

[0010] Train the joint learning model based on the constructed training sample set to obtain a trained joint learning model;

[0011] Input the feature data of the drug and adverse reaction to be predicted into the trained joint learning network to predict whether the drug will cause the adverse reaction.

[0012] Based on a further improvement of the above method, the following formula is used to calculate the loss of the joint learning model:

[0013] ;

[0014] where represents the prediction loss, Denote the parameters of the propensity score model, Denote the parameters of the adverse reaction prediction model, Denote the parameters of the delayed feedback prediction model, Denote the regularization parameter, Denote the 2-norm of the matrix.

[0015] Based on the further improvement of the above method, the prediction loss is calculated using the following formula:

[0016] ;

[0017] where, Denote the prediction result of the propensity score model for the i-th drug-adverse reaction pair, Denote the prediction result of the adverse reaction prediction model for the i-th drug-adverse reaction pair, Denote the prediction result of the delayed feedback prediction model for the i-th drug-adverse reaction pair, Denote the delayed feedback time of the i-th drug-adverse reaction pair; Denote the observation time when the i-th drug-adverse reaction pair is observed; Denote the feature data of the i-th drug-adverse reaction pair, Denote that the i-th drug-adverse reaction pair is a positive sample, Denote that the i-th drug-adverse reaction pair is a negative sample.

[0018] Based on the further improvement of the above method, the propensity score model uses the following formula to calculate the prediction result of the i-th drug-adverse reaction pair:

[0019] ;

[0020] where, Denote the feature data of the i-th drug-adverse reaction pair, Denote the parameters of the propensity score model.

[0021] Based on the further improvement of the above method, the adverse reaction prediction model uses the following formula to calculate the prediction result of the i-th drug-adverse reaction pair:

[0022] ;

[0023] where, Denote the feature data of the i-th drug-adverse reaction pair, Denote the parameters of the adverse reaction prediction model.

[0024] Based on the further improvement of the above method, the delayed feedback prediction model models the delayed feedback time of the i-th drug-adverse reaction pair using the following formula:

[0025] ;

[0026] wherein, represents the characteristic data of the i-th drug-adverse reaction pair, represents the parameter of the delayed feedback prediction model.

[0027] On the other hand, an embodiment of the present invention provides a drug adverse reaction prediction system with delayed feedback, including:

[0028] A sample set construction module, configured to obtain the characteristic data and observation data of drugs and adverse reactions, and construct a training sample set;

[0029] A model construction module, configured to construct a joint learning model, and the joint training model includes: a propensity score model, configured to predict the probability that a drug-adverse reaction is observed; an adverse reaction prediction model, configured to predict the probability that a drug produces an adverse reaction; a delayed feedback prediction model, configured to predict the delayed feedback time of an adverse reaction;

[0030] A model training module, configured to train the joint learning model based on the constructed training sample set to obtain a trained joint learning model;

[0031] A prediction module, configured to input the characteristic data of the drug and adverse reaction to be predicted into the trained joint learning network to predict whether the drug will cause the adverse reaction.

[0032] Based on the further improvement of the above system, the following formula is used to calculate the loss of the joint learning model:

[0033] ;

[0034] wherein, represents the prediction loss, represents the parameter of the propensity score model, represents the parameter of the adverse reaction prediction model, represents the parameter of the delayed feedback prediction model, represents the regularization parameter, represents the 2-norm of the matrix.

[0035] Based on the further improvement of the above system, the following formula is used to calculate the prediction loss:

[0036] ;

[0037] wherein, represents the prediction result of the propensity score model for the i-th drug-adverse reaction pair, represents the prediction result of the adverse reaction prediction model for the i-th drug-adverse reaction pair, represents the prediction result of the delayed feedback prediction model for the i-th drug-adverse reaction pair, represents the delayed feedback time of the i-th drug-adverse reaction pair; represents the observation time when the i-th drug-adverse reaction pair is observed; represents the feature data of the i-th drug-adverse reaction pair, represents that the i-th drug-adverse reaction pair is a positive sample, represents that the i-th drug-adverse reaction pair is a negative sample.

[0038] Based on the further improvement of the above system, the adverse reaction prediction model calculates the prediction result of the i-th drug-adverse reaction pair using the following formula:

[0039] ;

[0040] where, represents the feature data of the i-th drug-adverse reaction pair, represents the parameters of the adverse reaction prediction model.

[0041] Compared with the prior art, the present invention constructs a training sample set by obtaining the feature data and observation data of drugs and adverse reactions, constructs a joint learning model including a propensity score model, an adverse reaction prediction model, and a delayed feedback prediction model, reduces the influence of selection bias through the propensity score model, makes the finally learned prediction model more robust in the face of selection bias, improves the accuracy of adverse reaction prediction through multi-task learning that simultaneously optimizes adverse reaction prediction and delayed feedback prediction, provides unbiased adverse reaction prediction in scenarios with both selection bias and delayed feedback, and further improves the prediction accuracy.

[0042] In the present invention, the above technical solutions can also be combined with each other to achieve more preferred combination schemes. Other features and advantages of the present invention will be described in the subsequent specification, and some advantages can be made obvious from the specification, or understood by implementing the present invention. The objectives and other advantages of the present invention can be realized and obtained through the content specifically pointed out in the specification and the drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] The drawings are only for the purpose of showing specific embodiments and are not considered to be a limitation of the present invention. Throughout the drawings, the same reference signs represent the same components;

[0044] Figure 1 is a flowchart of a method for predicting drug adverse reactions with delayed feedback according to an embodiment of the present invention;

[0045] Figure 2This is a block diagram of a drug adverse reaction prediction system with delayed feedback in an embodiment of the present invention. Detailed implementation manners

[0046] The preferred embodiments of the present invention will be specifically described below with reference to the accompanying drawings. The accompanying drawings form a part of this application and are used together with the embodiments of the present invention to explain the principles of the present invention, rather than to limit the scope of the present invention.

[0047] A specific embodiment of the present invention discloses a drug adverse reaction prediction method with delayed feedback, as Figure 1 shown, which includes the following steps:

[0048] Obtain the characteristic data and observation data of drugs and adverse reactions, and construct a training sample set;

[0049] Construct a joint learning model, and the joint training model includes: a propensity score model for predicting the probability that a drug-adverse reaction is observed; an adverse reaction prediction model for predicting the probability that a drug produces an adverse reaction; a delayed feedback prediction model for predicting the delayed feedback time of an adverse reaction.

[0050] Train the joint learning model based on the constructed training sample set to obtain a trained joint learning model;

[0051] Input the characteristic data of the drug and adverse reaction to be predicted into the trained joint learning network to predict whether the drug will cause the adverse reaction.

[0052] Compared with the prior art, the drug adverse reaction prediction method with delayed feedback provided in this embodiment constructs a training sample set by obtaining the characteristic data and observation data of drugs and adverse reactions, constructs a joint learning model including a propensity score model, an adverse reaction prediction model, and a delayed feedback prediction model, reduces the influence of selection bias through the propensity score model, makes the finally learned prediction model more robust in the face of selection bias, improves the accuracy of adverse reaction prediction through multi-task learning that simultaneously optimizes adverse reaction prediction and delayed feedback prediction, provides unbiased adverse reaction prediction in scenarios with both selection bias and delayed feedback, and further improves the prediction accuracy.

[0053] The method of the present invention can accurately predict adverse drug reactions, which can help identify possible side effects at an early stage, thereby reducing the risk of serious adverse reactions after the drug is marketed. This helps protect the health of patients and reduce medical accidents caused by drugs. By predicting adverse reactions at an early stage of drug development, pharmaceutical companies can more effectively screen and optimize candidate drugs, reducing the risk of failure. This can save R & D costs and time and improve the efficiency of drug R & D. Accurately predicting adverse drug reactions before clinical trials can help design safer trial protocols, select appropriate dose ranges and subjects, thereby reducing the risk in trials and increasing the success rate of trials. In addition, by predicting the adverse reactions of different individuals to drugs, it can help doctors formulate personalized medication plans according to the individual characteristics of patients (such as genetic information, previous medical history, etc.), thereby improving the treatment effect and reducing adverse reactions.

[0054] In the following, uppercase letters are used to represent random variables, and lowercase letters are used to represent the corresponding data. The variable definitions are as follows (for simplicity, subscript i is omitted in some formulas):

[0055] X represents the set of features, including the features of drugs and adverse reactions, represents the feature data of the i-th drug-adverse reaction pair.

[0056] represents whether the drug-adverse reaction pair is reported.

[0057] represents the true label of the drug-adverse reaction pair.

[0058] : represents the time from taking the drug to the occurrence of an adverse reaction, that is, the delayed feedback time.

[0059] : the observation time after taking the drug.

[0060] represents whether an adverse reaction occurred during the observation time.

[0061] Drugs and adverse reactions constitute drug-adverse reaction pairs.

[0062] The observed data includes whether the i-th drug-adverse reaction pair is reported , the true label , the observation time , the observed outcome , the delayed time of the occurrence of the adverse reaction .

[0063] In implementation, the characteristic data of the drug-adverse reaction pair can be extracted according to the information of the drug and the adverse reaction information. For example, the drug and the adverse reaction are respectively coded, and the combination of the drug code and the adverse reaction code constitutes the characteristic data of the drug-adverse reaction pair.

[0064] Different from the prior art, the present invention does not need to assume that are independent of each other under the given characteristics and . At the same time, the present invention assumes that is independent of the observation time G. This assumption holds because the observation time is determined by the characteristics of the patient (for example, when the patient stays in the hospital), while whether an adverse reaction occurs and the time of occurrence of the adverse reaction are determined by the essential characteristics of the drug and the patient.

[0065] From the data set, the time (time to complete the transformation) when the observed drug-adverse reaction pair produces an adverse reaction can be obtained , characteristic data and the observation time . Denote the entire data set as , and the set of observed drug-adverse reaction pairs as The observed data consists of the characteristic , the observation outcome , and the observation time . For the case of the observation outcome , the delayed feedback time from taking the medicine to the occurrence of the adverse reaction can be further obtained .

[0066] Therefore, by obtaining the characteristic data and the observation data of the drug and the adverse reaction, each sample in the constructed training sample set includes the characteristic data of the drug-adverse reaction pair , the observation time , the observation outcome , and the positive sample of the observation outcome also includes the delay time of the occurrence of the adverse reaction .

[0067] In implementation, the present invention assumes that the probability distribution of the delay time follows an exponential distribution, and the risk function of the delayed feedback is expressed as . Under the exponential distribution, due to the delayed feedback factor, for the drug-adverse reaction pair with the characteristic , the probability that the adverse reaction is not observed is .

[0068] In implementation, in order to improve the accuracy of drug adverse reaction prediction, the present invention constructs a joint learning model, and the joint learning model includes a propensity score model, an adverse reaction prediction model, and a delayed feedback prediction model.

[0069] In implementation, to address the selection bias problem, the joint learning model of the present invention includes a propensity score model for predicting the probability that a drug - adverse reaction is reported.

[0070] In implementation, a logistic regression model is used to construct the propensity score model.

[0071] Specifically, the propensity score model calculates the prediction result of the i - th drug - adverse reaction pair using the following formula:

[0072] ;

[0073] where, represents the feature data of the i - th drug - adverse reaction pair, represents the parameters of the propensity score model. That is, the probability that the i - th drug - adverse reaction is reported calculated by the propensity score model.

[0074] In implementation, the probability that the i - th drug - adverse reaction is reported is calculated by formula (1).

[0075] In implementation, to further fit the observed data, the present invention uses an exponential distribution to model the delayed feedback time.

[0076] In implementation, an exponential distribution is used to construct the delayed feedback prediction model; the delayed feedback prediction model calculates the delayed feedback time of the i - th drug - adverse reaction pair using the following formula:

[0077] ;

[0078] where, represents the feature data of the i - th drug - adverse reaction pair, represents the parameters of the delayed feedback prediction. That is, the exponential distribution parameter corresponding to the delayed feedback time of the i - th drug - adverse reaction pair predicted by the delayed feedback prediction model.

[0079] An adverse reaction prediction model for predicting the probability that a drug produces an adverse reaction.

[0080] In implementation, a logistic regression model is used to construct the adverse reaction prediction model; the adverse reaction prediction model calculates the prediction result of the i - th drug - adverse reaction pair using the following formula:

[0081] ;

[0082] where, represents the feature data of the i - th drug - adverse reaction pair, represents the parameters of the adverse reaction prediction. That is, the probability of an adverse reaction occurring for the i-th drug-adverse reaction pair calculated by the adverse reaction prediction model.

[0083] By constructing a joint learning model and performing multi-task learning, the present invention enables multiple tasks to assist each other, and can improve the accuracy of drug adverse reaction prediction in the presence of delayed feedback and selection bias.

[0084] In implementation, the present invention uses the following formula to calculate the loss of the joint learning model:

[0085] ;

[0086] Wherein, represents the prediction loss, represents the parameters of the propensity score model, represents the parameters of the adverse reaction prediction model, represents the parameters of the delayed feedback prediction model, represents the regularization parameter, represents the 2-norm of the matrix. is the negative log-likelihood function.

[0087] To prevent overfitting and improve the stability of the model, the training loss of the joint learning model includes regularization terms of the propensity score model, the adverse reaction prediction model, and the delayed feedback prediction model .

[0088] For the i-th drug-adverse reaction pair, if it is finally observed that the drug has produced the adverse reaction, that is , this means that the drug-adverse reaction pair has been reported, that is , and the true label of the drug-adverse reaction pair is positive , the time when the adverse reaction is observed is , , represents the observation time of the i-th drug-adverse reaction pair.

[0089] For the i-th drug-adverse reaction pair, if it is finally not observed to produce the adverse reaction, that is , then there are the following three cases: the drug does not have the adverse reaction, that is ; the drug has the adverse reaction but is not reported ( , ); the drug has the adverse reaction and is reported, but the adverse reaction is not produced within the observation time, resulting in a negative sample being reported ( , , ).

[0090] Therefore, for For a positive sample, the probability of observing an adverse drug reaction within the observation time is the product of the probability of observing a drug - adverse reaction pair, the probability of the drug causing an adverse reaction, and the probability that the time of onset of the adverse reaction is less than or equal to the observation time. Taking the logarithm of this product gives the loss for the positive sample. 。

[0091] For a negative sample, the probability of not observing an adverse drug reaction within the observation time is the sum of the following three probabilities: not observing a drug - adverse reaction pair; observing a drug - adverse reaction pair but no adverse reaction occurred; observing a drug - adverse reaction pair and an adverse reaction occurred, but the time of onset of the adverse reaction exceeded the observation time. Therefore, for the negative sample, its loss is

[0092] 。

[0093] Therefore, the following formula is used to calculate the prediction loss:

[0094] ;

[0095] where represents the prediction result of the propensity score model for the i - th drug - adverse reaction pair, represents the prediction result of the adverse reaction prediction model for the i - th drug - adverse reaction pair, represents the prediction result of the delayed feedback prediction model for the i - th drug - adverse reaction pair, represents the delayed feedback time of the i - th drug - adverse reaction pair; represents the observation time of observing the i - th drug - adverse reaction pair; represents the feature data of the i - th drug - adverse reaction pair, represents that the i - th drug - adverse reaction pair is a positive sample, represents that the i - th drug - adverse reaction pair is a negative sample.

[0096] When directly maximizing the traditional likelihood function on the sample, due to the existence of selection bias and delayed feedback, the prediction results may be biased. The present invention improves the likelihood function and optimizes the improved likelihood function through multi - task learning to simultaneously handle selection bias and delayed feedback, thereby obtaining a more accurate drug adverse reaction prediction model.

[0097] A specific embodiment of the present invention discloses a drug adverse reaction prediction system with delayed feedback, as Figure 2 shown, the system includes:

[0098] A sample set construction module for obtaining the feature data and observation data of drugs and adverse reactions and constructing a training sample set;

[0099] A model construction module, configured to construct a joint learning model, where the joint training model includes: a propensity score model, configured to predict the probability that a drug-adverse reaction is observed; an adverse reaction prediction model, configured to predict the probability that a drug produces an adverse reaction; and a delayed feedback prediction model, configured to predict the delayed feedback time of the adverse reaction.

[0100] A model training module, configured to train the joint learning model based on the constructed training sample set to obtain a trained joint learning model.

[0101] A prediction module, configured to input the feature data of the drug and the adverse reaction to be predicted into the trained joint learning network to predict whether the drug will cause the adverse reaction.

[0102] Preferably, the following formula is used to calculate the loss of the joint learning model:

[0103] ;

[0104] where represents the prediction loss, represents the parameters of the propensity score model, represents the parameters of the adverse reaction prediction model, represents the parameters of the delayed feedback prediction model, represents the regularization parameter, represents the 2-norm of the matrix.

[0105] Preferably, the following formula is used to calculate the prediction loss:

[0106] ;

[0107] where represents the prediction result of the propensity score model for the i-th drug-adverse reaction pair, represents the prediction result of the adverse reaction prediction model for the i-th drug-adverse reaction pair, represents the prediction result of the delayed feedback prediction model for the i-th drug-adverse reaction pair, represents the delayed feedback time of the i-th drug-adverse reaction pair; represents the observation time when the i-th drug-adverse reaction pair is observed; represents the feature data of the i-th drug-adverse reaction pair, represents that the i-th drug-adverse reaction pair is a positive sample, represents that the i-th drug-adverse reaction pair is a negative sample.

[0108] Preferably, the following formula is used by the adverse reaction prediction model to calculate the prediction result of the i-th drug-adverse reaction pair:

[0109] ;

[0110] wherein, represents the characteristic data of the i-th drug-adverse reaction pair, represents the parameters of the adverse reaction prediction model.

[0111] The above method embodiments and system embodiments are based on the same principle, and their related parts can be learned from each other and can achieve the same technical effects. For the specific implementation process, please refer to the foregoing embodiments and will not be elaborated here.

[0112] Embodiment of electronic device:

[0113] A specific embodiment of the present application discloses an electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the program, it implements the steps of the drug adverse reaction prediction method with delayed feedback in the method embodiment.

[0114] Embodiment of readable storage medium:

[0115] A specific embodiment of the present application discloses a non-transitory computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, it implements the steps of the drug adverse reaction prediction method with delayed feedback in the method embodiment.

[0116] Those skilled in the art can understand that all or part of the processes of implementing the above method embodiments can be completed by instructing relevant hardware through a computer program, and the program can be stored in a computer-readable storage medium. Among them, the computer-readable storage medium is a disk, an optical disk, a read-only memory, or a random access memory, etc.

[0117] The above is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed by the present invention should be covered by the protection scope of the present invention.

Claims

1. A method for predicting adverse drug reactions with delayed feedback, characterized in that: The following steps are involved: Obtain characteristic data and observation data of drugs and adverse reactions, and construct a training sample set; Constructing a joint learning model, the joint learning model includes: a propensity score model for predicting the probability of drug-adverse reactions being observed; an adverse reaction prediction model for predicting the probability of drug-adverse reactions; and a delayed feedback prediction model for predicting the delayed feedback time of adverse reactions; Training the joint learning model based on the constructed training sample set to obtain a trained joint learning model; Input the characteristic data of the drug to be predicted and the adverse reaction into the trained joint learning network to predict whether the drug will cause the adverse reaction; The propensity score model uses the following formula to calculate the prediction result of the ith drug-adverse reaction pair: ； in, represents the characteristic data of the ith drug-adverse reaction pair, represents the parameters of the propensity score model; The adverse reaction prediction model uses the following formula to calculate the prediction result of the ith drug-adverse reaction pair: ； in, represents the characteristic data of the ith drug-adverse reaction pair, represents the parameters of the adverse reaction prediction model; The delayed feedback prediction model uses the following formula to model the delayed feedback time of the ith drug-adverse reaction pair: ； in, represents the characteristic data of the ith drug-adverse reaction pair, Represents the parameters of the delayed feedback prediction model.

2. The method for predicting adverse drug reactions with delayed feedback according to claim 1, characterized in that: The loss of the joint learning model is calculated using the following formula: ； in, represents the prediction loss, represents the parameters of the propensity score model, represents the parameters of the adverse reaction prediction model, represents the parameters of the delayed feedback prediction model, represents the regularization parameter, Represents the 2-norm of a matrix.

3. The method for predicting adverse drug reactions with delayed feedback according to claim 2, characterized in that: The prediction loss is calculated using the following formula: ； in, represents the prediction result of the propensity score model for the i-th drug-adverse reaction pair, represents the prediction result of the adverse reaction prediction model for the i-th drug-adverse reaction pair, represents the prediction result of the delayed feedback prediction model for the i-th drug-adverse reaction pair, represents the delayed feedback time of the ith drug-adverse reaction pair; represents the observation time of the i-th drug-adverse reaction pair; represents the characteristic data of the ith drug-adverse reaction pair, Indicates that the i-th drug-adverse reaction pair is a positive sample, Indicates that the i-th drug-adverse reaction pair is a negative sample.

4. A drug adverse reaction prediction system with delayed feedback, characterized in that: include: The sample set construction module is used to obtain the characteristic data and observation data of drugs and adverse reactions and construct the training sample set; A model building module is used to build a joint learning model, wherein the joint learning model includes: a propensity score model, which is used to predict the probability of drug-adverse reactions being observed; an adverse reaction prediction model, which is used to predict the probability of adverse reactions caused by drugs; and a delayed feedback prediction model, which is used to predict the delayed feedback time of adverse reactions; A model training module, used to train the joint learning model based on the constructed training sample set to obtain a trained joint learning model; A prediction module is used to input the characteristic data of the drug to be predicted and the adverse reaction into the trained joint learning network to predict whether the drug will cause the adverse reaction; The propensity score model uses the following formula to calculate the prediction result of the ith drug-adverse reaction pair: ； in, represents the characteristic data of the ith drug-adverse reaction pair, represents the parameters of the propensity score model; The adverse reaction prediction model uses the following formula to calculate the prediction result of the ith drug-adverse reaction pair: ； in, represents the characteristic data of the ith drug-adverse reaction pair, represents the parameters of the adverse reaction prediction model; The delayed feedback prediction model uses the following formula to model the delayed feedback time of the ith drug-adverse reaction pair: ； in, represents the characteristic data of the ith drug-adverse reaction pair, Represents the parameters of the delayed feedback prediction model.

5. The drug adverse reaction prediction system with delayed feedback according to claim 4, characterized in that: The loss of the joint learning model is calculated using the following formula: ； in, represents the prediction loss, represents the parameters of the propensity score model, represents the parameters of the adverse reaction prediction model, represents the parameters of the delayed feedback prediction model, represents the regularization parameter, Represents the 2-norm of a matrix.

6. The drug adverse reaction prediction system with delayed feedback according to claim 5, characterized in that: The prediction loss is calculated using the following formula: ； in, represents the prediction result of the propensity score model for the i-th drug-adverse reaction pair, represents the prediction result of the adverse reaction prediction model for the i-th drug-adverse reaction pair, represents the prediction result of the delayed feedback prediction model for the i-th drug-adverse reaction pair, represents the delayed feedback time of the ith drug-adverse reaction pair; represents the observation time of the i-th drug-adverse reaction pair; represents the characteristic data of the ith drug-adverse reaction pair, Indicates that the i-th drug-adverse reaction pair is a positive sample, Indicates that the i-th drug-adverse reaction pair is a negative sample.

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